I would imagine it shouldn't make much of a difference because if your scores are what you say they are, which is pretty good, you shouldn't have difficulty getting the Walmart card. If for whatever reason they have a problem with the recency of your BK, that would probably be the case with the pre-approval as well. Other popular store cards you may want to try are Target, Kay Jeweler's, and Macy's.
As others have said, try the BoA and Cap1 pre-approvals. If Cap1 was IIB, do not cold apply for them. You can try a cold app on BoA, however, and hope that they counter-offer their 99/500 card, which you can find plenty of information about here. You can also try a secured card through BoA, CITI, and certain other issuers but do your research first and try to find one that will eventually unsecure and grow with you over time.
Another option would be to apply with a CU. You can find lots of information about those on the BK friendly thread.
Worst case scenario, look into the various HSBC offerings such as Orchard Bank, Household, or even direct from HSBC. Most of their applications are pre-qualifiers so you can see how you like the terms before you apply. Both their secured and unsecured cards are quite easy to get. Try to find something with no or minimal annual fee.
Good luck!